Semi-Empirical Inverse Model for DX Unit Performance in Residential Buildings

Inverse models are generally derived from empirical behavior and expressed in terms of one or more driving forces and a set of empirical parameters that are “identified” using measurements. Once identified, a model can be used for a variety purposes, including performance monitoring, diagnostics, retrofit analysis, measurement and verification of efficiency improvements, and on-line control optimization. In this paper, a semi-empirical inverse model or a “grey-box” model is developed to estimate the power consumption of a direct expansion (DX) air conditioning system that handles the cooling requirement of a residential building. This “grey-box” model approach requires fewer parameters and training data and provides better extrapolation than other popular empirical or “black-box” models. The model is based on physical system performance parameters and not only on a single compressor or coil, so it can provide a clear performance map of the air conditioning system in residential buildings. The training and validation data used for model construction in this paper comes from manufacturer’s detailed DX unit performance models, which closely matches equipment performance in the field. NOMENCLATURE C: Clearance volume factor P: Refrigerant pressure V: Displacement volume T: Temperature RPM: Motor angular speed TC: Refrigerant critical temperature a, b, d, e, f, ∆p, A, B: Constant parameters PC: Refrigerant critical pressure n: Polytropic exponent ∆P: Pressure difference across the compressor Cp: Specific heat at constant pressure Cv: Specific heat at constant volume N: data set number m: mass flow rate SUBSCRIPTS out: Outside in: Inside room dis: Discharge suc: Suction evap or e: evaporating cond or c: Condensing db: dry bulb wb: wet bulb real: Measured mean: Average value cal: calculated